Question

What is the smallest natural number that should be multiplied with $840$ to make it a perfect square?

Answer 1

$840=84\times 10$
$840=4\times 21\times 2\times 5$
$840=2^3\times 7\times 3\times 5$

To make it a perfect square it should be multiplied with $2\times 7\times 3\times 5$ so that powers of prime numbers will become even.

$2\times 7\times 3\times 5=14\times 15$

$=210$